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Let's says I have unequal monthly interest rates (1,5% in the first month, 1,7% in the second, -0,8% in the third...) is there a way I can calculate what was my interest rate in the semester or in the year? On all the formulas I could manage to find it is taken into consideration that monthly rates are always the same.

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  • It'd be easiest to handle this in a spreadsheet where you can copy down, or in a script that can loop over the changing rates, but an annualized rate would be calculated with: APY = (1+r1)*(1+r2) *(1+r3) *(1+r4) *(1+r5) *(1+r6) *(1+r7) *(1+r8) *(1+r9) *(1+r10) *(1+r11) *(1+r12) – 1 where r1-r12 are the 12 different monthly rates. If you're talking about variable rate debt, then the above neglects compounding interest.
    – Hart CO
    Jan 16, 2018 at 18:45
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    @Hartco Any reason that comment shouldn't be an answer?
    – Rupert Morrish
    Jan 16, 2018 at 21:16
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    @RupertMorrish I suspected they need to incorporate compounding and I didn't want to fuss with showing what the copy-down formula would be in Excel.
    – Hart CO
    Jan 16, 2018 at 21:50
  • @HartCO Should be 1+(r1/12) and so on, assuming the interest rates are quoted as annual rates, which they almost certainly are.
    – David Schwartz
    Jan 17, 2018 at 0:30

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You can use the geometric mean, e.g.

enter image description here

Check

quarterly return = (1 + 0.015)*(1 + 0.017)*(1 - 0.008) - 1 = 2.3997 %

Using the geometric mean

gm = 1.007935842

quarterly return = gm^3 - 1 = 2.3997 %

So the average monthly return is gm - 1 = 0.7935842 %

The effective annual interest rate would be gm^12 - 1 = 9.94986 % and the nominal annual rate compounded monthly would be (gm - 1)*12 = 9.52301 %.

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